#01Nov 12, 2026
cs.CL
Goal Encoding in LLMs
Arnab Sen Sharma, Eric Todd, Sheridan Feucht and 7 more
We investigate whether and how LLMs encode goals: internal neural representations that precede and guide action, and that are flexible enough to be realized through many different execution paths. We construct a coding setting with multiple sub-tasks that allows us to evaluate goal-seeking behavior and the selection of sub-goals. In this setting, we localize an encoding of the next sub-goal in the outputs of a sparse set of attention heads. The same heads can be used to decode the LM's future actions in natural language (e.g., "I'm checking if a word is a palindrome"). We verify that this encoding is causal for next action and is plastic: transplanting it into a different environment, e.g., another programming language, triggers the same operation realized with a different sequence of tokens. The LM also sustains the encoding throughout the action's execution, which is puzzling because a transformer LM without recurrence cannot carry a state forward for more tokens than it has layers left. We propose that it does not need to. Under a non-recurrent goal-seeking (NRGS) account, the LM frequently re-reads the goal from the task specification, compares it with the progress visible in the growing context, and pursues what remains. We test the predictions of this account with targeted causal interventions.
#02Nov 12, 2026
cs.AI
Classical Energies Learn to Reason 1,000x Faster than Looped Models
Benjamin Hoover, Hugh Blayney, James C. R. Whittington
Looped models have emerged as a prominent paradigm for reasoning, with successes on simple reasoning puzzles such as Sudoku-Extreme and Maze-Unique. However, these models can be unstable, slow to train, and use many parameters and FLOPs to solve simple puzzles. Descent on an energy not only mitigates these issues but also offers advantages: built-in early stopping, compute that adapts to problem difficulty, fast training without differentiating through a solver, and interpretable weights that learn the constraints of the puzzle. Here we demonstrate this with a learned version of Hopfield & Tank's energy from the 80s, which we term CRAM, solves 99.996% of Sudoku-Extreme and 100% of Maze-Unique test puzzles after 42 ms and 132 ms of training on one GPU, at least 1,000x faster than looped models on these tasks. CRAM also matches baseline looped models at their highest accuracy on Sudoku-Extreme using at least 282x fewer inference FLOPs. Our work suggests two things. First, that energies are an extremely promising direction for training reasoning from data. Second, a caution against using trivially solvable benchmarks like Sudoku and Maze to test the scalability of looped reasoning techniques.
#03Nov 12, 2026
stat.ML
Quantifying structural stability of transparent models for general insurance pricing
Félix Côté, Marie-Pier Côté
The short duration of general insurance contracts leads to rapid distributional shifts in the data, warranting regular model updates. This process may yield a post-update model that differs considerably from the pre-update model in both predictions and structure. Structural stability is upstream of predictive stability, yet existing structural stability metrics are mostly restricted to simple decision trees. Thus, we first introduce the notion of functional transparency, characterising models with a prediction function that can be expressed as a sum of univariate functions for main effects and bivariate functions for pairwise interactions. Then, we propose the Mean Squared Shape function distance, a metric to quantify the structural stability of functionally transparent models, which are particularly relevant in actuarial science. Using three public auto insurance datasets, we present a benchmark study to demonstrate the usefulness of our metric in identifying a stable and accurate transparent model. Generalised linear models with centred numerical covariates are stable, and explainable boosting machines (EBMs) offer a compromise between stability and performance. We also find that stabilisation strategies, such as sequential modelling and fixed hyperparameters, can substantially improve stability for both EBM and XGBoost models, with negligible impact on performance.
#04Nov 12, 2026
cs.DS
Sketching Language Models for Context Attribution
Christopher Liaw, Aranyak Mehta, Grigoris Velegkas and 1 more
Context attribution asks how removing parts of a prompt changes a language model's output. We study leave-one-out (LOO) attribution for a prompt of $n$ tokens and a fixed measurement function. Computing all LOO values directly requires $n$ model evaluations. Under a stability assumption, our algorithm estimates all LOO values to error proportional to $\varepsilon$ with constant probability using $O(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ evaluation calls. To complement our upper bound, we prove a matching $Ω(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ lower bound on the number of evaluation calls in an oracle model. Empirically, we verify coefficient decay consistent with stability and evaluate the performance of our sketching algorithm on a small language-model retrieval task. Technically, our result is based on a sketching algorithm for arithmetic circuits whose Taylor coefficients satisfy the stability condition recently introduced by Gunn [Gun26]. A direct adaptation of their forward differentiation sketches would require $\widetilde{O}(\log(n)/\varepsilon^2)$ evaluation calls. Our key observation is that we can apply forward differentiation to the backpropagation circuit, with only constant overhead over a forward sketch of the same Taylor degree. This reduces the variance of the sketches and is key to our improved evaluation bound. Our lower bound builds on the techniques of Amsel, Chen, Duman Keles, Halikias, Musco, and Musco [ACDH+26, SIAM Journal on Matrix Analysis and Applications] for lower bounding the number of matrix-vector queries to estimate the diagonal elements of random matrices.
#05Nov 12, 2026
cs.CV
Unbundling Multimodal Vision Encoding
Ellis Brown, Chris Hoang, Shengyi Qian and 9 more
How multimodal language models should encode visual input remains up for debate. Most models use a pretrained vision encoder, while some recent recipes train the encoder from scratch with the language model or remove it entirely. Vision encoders bundle together three design choices: a visual prior from upstream pretraining, dedicated vision capacity, and pre-fusion placement of that capacity (i.e., before the multimodal backbone). Because published models also differ in data, architecture, and compute, comparing them cannot isolate the effect of each choice. We disentangle these choices via a controlled framework where we pretrain all models from scratch on common data and compare them on visual question answering and language benchmarks at matched lifetime compute. We find that the visual prior is not necessary; an encoder trained jointly from scratch is on par with a pretrained one, without a separate training stage. What matters instead is dedicated vision capacity: an encoder-free model trails on visual understanding even when its backbone is enlarged by the encoder's parameter count. Yet that capacity need not precede multimodal fusion, as vision-only modules added in-fusion to early backbone layers perform comparably to a pre-fusion encoder and can lower time to first token. These results also hold across backbone sizes, when encoder pretraining is treated as free, and when starting from a pretrained language model. Overall, our findings favor dedicated vision capacity trained jointly with the backbone and placed early within it.